Leveraging LLMs to Enrich Mathematics Teaching:Interactive Tools, Enhanced Content, and Improved Student Learning

17th ICME · Dynamic Conference PresentationJune 12-14, 2026 · MGM University · Aurangabad, Maharashtra, India

Paper presentation · International Conference on Multidisciplinary Education

Leveraging LLMs to Enrich Mathematics Teaching

Interactive Tools, Enhanced Content, and Improved Student Learning

Dr. Vignon OussaDepartment of Mathematics · Bridgewater State University
Dr. Mahmoud El-HashashDepartment of Mathematics · Bridgewater State University

A cinematic synthesis of concept-dependency mapping, gateway feedback, Mathematica laboratories, and MATLAB-validated hybrid optimization workflows.

Instructor
Judgmentcontrol layer
Structurevisible
Toolsinteractive
Feedbackformative
Validationcomputed
Learningevidence

Central claim

LLMs make careful instructional design more visible, more responsive, and more testable.

The claim is not automation. The claim is amplification: course structure becomes explicit, bottlenecks become addressable, and student feedback becomes more timely under instructor review.

Not the model

Autonomous grading

LLMs are not used as independent graders, replacements for mathematical proof standards, or final arbiters of student work.

The model

Design amplification

LLMs draft, reorganize, translate, and scaffold materials so that the instructor can work more precisely.

The safeguard

Human verification

The instructor remains responsible for correctness, context, fairness, privacy, and final judgment.

Thesis: AI strengthens mathematics teaching when it amplifies structure, clarity, computation, timely feedback, and evidence-driven revision.

The talk as a system

Three classroom and research systems, one transferable workflow

1
MATH 261Concept dependency graph → bottleneck gateways → individualized feedback reports.
→
2
Applied MathematicsTheory session → LLM-organized Mathematica lab → computational reflection.
→
3
Hybrid OptimizationLLM-assisted code drafts → MATLAB execution → validated comparison package.

Interactive tools

Concept Analyzer, gateway reports, Mathematica labs, and MATLAB comparison scripts.

Enhanced content

Theory notes become guided activities, focused assessments, and runnable computational experiments.

Improved learning

Evidence from student work and computation informs redesign instead of ending at a grade.

Responsible AI standard

The instructor is the control layer.

The LLM can accelerate drafting, mapping, and transformation. It cannot carry the mathematical responsibility of the course.

1
Correctness

Every graph, gateway, solution, lab, and script is reviewed against mathematical standards.

2
Context

The instructor interprets prerequisites, course goals, and actual student evidence.

3
Restraint

Feedback is formative, anonymized where appropriate, and not outsourced as final grading.

Instructor
oversight
LLM draftsdraft layer
Toolsinteraction layer
Evidencestudent layer
Validationmath layer

Case Study 1 · MATH 261 Multivariable Calculus

From concept list to dependency graph

The key question: does concept A need to be understood before concept B can be learned responsibly?

Gateway AVectorsDot product Gateway BGradient Gateway CDoubleintegrals Planesgeometry Workprojection Lineintegrals Directionalderivatives Tangentplanes Optimization Boundsregions Polar +triple

Focused assessment design

Three gateway exams turn bottlenecks into non-punitive checkpoints.

Gateway A · Operational mastery

Students demonstrate vector construction, dot products in context, work versus component, and precise language.

Target bottleneck

Vectors and dot product.

→
Feedback emphasis

Setup, computation, interpretation, and mathematical language.

Gateway B · Stable gradient workflow

Students compute ∇f, evaluate at the point, normalize the direction, take the dot product, and interpret.

Target bottleneck

Partial derivatives, gradient evaluation, and directional derivative.

→
Feedback emphasis

A repeatable workflow from computation to interpretation.

Gateway C · Geometry before computation

Students separate integration skill from region interpretation, bounds, order of integration, volume, and accumulation.

Target bottleneck

Double-integral setup and region type.

→
Feedback emphasis

Correct bounds, correct region reading, and meaningful setup.

From student work to next steps

Feedback becomes a loop, not a terminal grade.

Student work Instructorgrading LLM draftfeedback Instructorreview Student reportnext steps Progressmap

Case Study 2 · Applied Mathematics

Theory becomes a guided computational lab.

LLMs help reorganize mathematical content into lab-ready prompts; Mathematica makes symbolic, numerical, and graphical evidence visible.

1
Meeting 1: theory

Definitions, examples, derivations, and mathematical discussion.

2
Between meetings: transformation

Notes are reorganized into guided prompts, tasks, and computational checks.

3
Meeting 2: Mathematica lab

Students connect symbolic, numerical, and graphical evidence.

Mathematica Lab Notebook
Prompt: Translate the theory example into symbolic, numeric, and graphical tests.
Symbolic: Simplify[model assumptions] → theorem structure
Numeric: Evaluate parameter cases → pattern detection

Mathematical learning through multiple representations

The lab is not decoration; it is evidence generation.

Students use computation to test, visualize, and interpret mathematical claims after the theory session.

Σ

Symbolic

Manipulate formulas, check identities, and connect syntax to mathematical structure.

#

Numerical

Explore parameter values, approximations, convergence behavior, and stability.

∿

Graphical

Make surfaces, curves, regions, and trends visible so that interpretation can be discussed.

Pedagogical purpose: LLMs help transform theory into computational exploration; Mathematica makes involved computations visible and testable.

Computational mathematics bridge

LLM output becomes a draft; MATLAB execution becomes the validation layer.

D

Research design

Define algorithms, benchmarks, bounds, and comparison questions.

→
AI

ChatGPT draft

Generate MATLAB code scaffolds and implementation variants.

→
M

MATLAB run

Execute, debug, plot, compare, and inspect numerical behavior.

→
✓

Validated package

24 runnable scripts with standardized metrics and plots.

Scientific stance: LLM-generated code is treated as a prototyping aid, not as final evidence. Execution, plots, tables, and repeated inspection supply validation.

Optimization principle

Hybridization coordinates two opposing forces.

ExplorationGlobal basin discovery
ExploitationLocal precision

Scenario 1 · Global-global hybridization

SA + GA improves robustness on multimodal landscapes.

GA

Population exploration

Selection, arithmetic crossover, and percentage-based mutation explore candidate regions.

→
★

Best GA candidate

The most promising population result becomes the handoff point.

→
SA

Stochastic refinement

Annealing accepts occasional uphill moves while cooling shifts toward intensification.

Rastrigin

Highly multimodal landscape for robustness testing.

Ackley

Flat outer region with many local minima.

Shubert

Multiple minima structure for challenging global search.

Scenario 2 · Global-local hybridization

PSO finds the basin; BFGS sharpens the solution.

PSO

Swarm discovery

Particles follow personal and global best positions to reduce sensitivity to initialization.

→
◎

Best particle

The best swarm point becomes the local-search starting point.

→
BFGS

Local intensification

Finite-difference gradients, line search, and curvature updates accelerate precision.

Ackley

Tests basin discovery before refinement.

Sphere

Clean convex baseline for convergence behavior.

Rosenbrock

Narrow curved valley stresses local refinement.

Validated package

24 scripts, 2 hybridization scenarios, 6 benchmark settings.

SA-GA scripts

Four codes per benchmark: SA, GA, hybrid, and comparison driver.

RastriginAckleyShubert

PSO-BFGS scripts

PSO runs first; the best swarm point initializes BFGS.

AckleySphereRosenbrock

Comparison layer

Standardized outputs make method-to-method evaluation interpretable.

tablesconvergence curvesbar charts
Best valuefinal solution quality
Best pointcomputed optimizer
CPU timecomputational cost
Iterationsalgorithmic effort
Curvestability and speed

Transferable workflow

A unified model: structure, computation, feedback.

The two classroom cases and the optimization case share a common design pattern: reveal structure, build targeted activities, use tools responsibly, and revise from evidence.

1
Map dependencies

Make hidden prerequisites visible.

2
Design targeted activity

Gateways and labs focus on high-leverage bottlenecks.

3
Validate and revise

Student evidence and computational evidence inform the next action.

Instructor
center
Map
Assess
Tool
Feedback
Revise

Closing

AI is most powerful when it makes mathematics teaching more intentional.

Keep the instructor at the center. Use LLMs to amplify structure, clarity, computation, and timely feedback.

The transferable move is simple: identify essential concepts, map dependencies, build focused assessments or labs, draft support materials with AI, review mathematically, anonymize responsibly, and revise instruction.

3connected teaching and research systems
24runnable MATLAB scripts in the optimization package
1instructor-centered design principle